Huidong Yang

Partitioned solvers for the fluid-structure interaction problems with a nearly incompressible elasticity model

In this paper, we present some analysis and numerical studies on two partitioned fluid-structure interaction solvers: a preconditioned GMRES solver and a Newton based solver, for the fluid-structure interaction problems employing a nearly incompressible elasticity model in a classical mixed displacement-pressure formulation. Both are highly relying on robust and efficient solvers for the fluid and structure sub-problems obtained from an extended and stabilized finite element discretization on hybrid meshes. A special algebraic multigrid method capable of handling such general saddle point systems for the incompressible and nearly incompressible models is investigated.

Partitioned solution algorithms for fluid-structure interaction problems with hyperelastic models

In this work, we consider fluid-structure interaction simulation with nonlinear hyperelastic models in the solid part. We use a partitioned approach to deal with the coupled nonlinear fluid-structure interaction problems. We focus on handling the nonlinearity of the fluid and structure sub-problems using (adaptive) Newtons method, the near-incompressibility of materials, the stabilization of employed finite element discretization, and the robustness and efficiency of Krylov subspace and algebraic multigrid methods for the linearized algebraic equations.

Robust and efficient monolithic fluid‐structure‐interaction solvers

In this note, we consider preconditioned Krylov subspace methods for discrete fluid-structure interaction problems with a nonlinear hyperelastic material model and covering a large range of flows, e.g, water, blood, and air with highly varying density. Based on the complete LDU factorization of the coupled system matrix, the preconditioner is constructed in form of L̂D̂Û , where L̂, D̂ and Û are proper approximations to L, D and U , respectively. The inverse of the corresponding Schur complement is approximated by applying one cycle of a special class of algebraic multigrid methods to the perturbed fluid sub-problem, that is obtained by modifying corresponding entries in the original fluid matrix with an explicitly constructed approximation of the exact perturbation coming from the sparse matrix-matrix multiplications.

A Newton Based Fluid–Structure Interaction Solver with Algebraic Multigrid Methods on Hybrid Meshes

Fluid–structure interaction problems arise in many application fields such as flows around elastic structures or blood flow problems in arteries. One method for solving such a problem is based on a reduction to an equation on the interface, involving the so-called Steklov–Poincare operators. This interface equation is solved by a Newton iteration for which directional derivatives with respect to the interface perturbation have to be evaluated appropriately. One step of the Newton iteration requires the solution of several decoupled linear sub-problems in the structure and the fluid domains. These sub-problems are spatially discretized by a finite element method on hybrid meshes containing different types of elements. For the time discretization implicit first-order methods are used for both sub-problems. The discretized equations are solved by algebraic multigrid methods.

Numerical simulation of fluid–structure interaction problems with hyperelastic models: A monolithic approach

In this paper, we consider a monolithic approach to handle coupled fluid-structure interaction problems with different hyperelastic models in an all-at-once manner. We apply Newtons method in the outer iteration dealing with nonlinearities of the coupled system. We discuss preconditioned Krylov sub-space, algebraic multigrid and algebraic multilevel methods for solving the linearized algebraic equations. Finally, we compare the results of the monolithic approach with those of the corresponding partitioned approach that we studied in our previous work.

GStokes: A Grid-enabled Solver for the 3D Stokes/Navier-Stokes System on Hybrid Meshes

Grid computing is a new framework for distributed computing that provides us a more advanced computing and memory resource sharing model for solving large scale computational problems. Under this environment, the challenging problem in computational fluid dynamics (CFD) can be resolved in an efficient way. However, the traditional solvers of partial differential equations (PDEs) using finite element method (FEM) are usually tight combinations of a mesh generator and a linear system solver, and thus not suitable for grid computing. In this paper, we present a newly designed grid-enabled client/server (CS) model for the 3D Stokes/Navier-Stokes problem on more complicated hybrid meshes. This paper mainly focuses on the construction of the client/server model under the grid environment, and how to apply it to the Stokes system.

An Algebraic Multigrid Method for an Adaptive Space–Time Finite Element Discretization

This work is devoted to numerical studies on an algebraic multigrid preconditioned GMRES method for solving the linear algebraic equations arising from a space–time finite element discretization of the heat equation using h–adaptivity on tetrahedral meshes. The finite element discretization is based on a Galerkin–Petrov variational formulation using piecewise linear finite elements simultaneously in space and time. In this work, we focus on h–adaptivity relying on a residual based a posteriori error estimation, and study some important components in the algebraic multigrid method for solving the space–time finite element equations.

4. Numerical methods for unsteady thermal fluid structure interaction

We discuss thermal fluid-structure interaction processes, where a simulation of the time-dependent temperature field is of interest. Thereby, we consider partitioned coupling schemes with a Dirichlet-Neumann method. We present an analysis of the method on a model problem of discretized coupled linear heat equations. This shows that for large quotients in the heat conductivities, the convergence rate will be very small. The time dependencymakes the use of time-adaptive implicitmethods imperative. This gives rise to the question as to how accurately the appearing nonlinear systems should be solved, which is discussed in detail for both the nonlinear and linear case. The efficiency of the resulting method is demonstrated using realistic test cases. (Less)

5. Recent development of robust monolithic fluid-structure interaction solvers

In the last few years, from the modeling point of view, the monolithic approach for fluid-structure interaction problems in many different application fields has been adopted by more and more researchers. Meanwhile, the development of monolithic solvers in the solution procedure for solving such coupled fluid-structure interaction problems all at once is in general a very hard task and has received a lot of attention. Due to the coupling conditions on the interface, it is challenging to design efficient preconditioners for the linearized coupled system of equations, that are robust with respect to the mesh size, time step size and material parameters. Further, it is nontrivial to realize scalable parallel implementations for solving such large scale coupled systems, which requires special care for handling the interface conditions. In this survey, we present an overview of some recent results on robust monolithic fluidstructure interaction solvers, that are mainly based on the block factorization, geometric and algebraic multigrid, and domain decomposition methods.

Algebraic Multigrid Based Preconditioners for Fluid-Structure Interaction and Its Related Sub-problems

This work is devoted to the development and testing of algebraic multigrid based preconditioners for the linearized coupled fluid-structure interaction problem using low order finite element basis functions, and the compressible and nearly incompressible elasticity sub-problems in mixed displacement-pressure form using higher-order finite element basis functions. The preconditioners prove to be robust with respect to the mesh size, time step size, and other material parameters.